43. Humility in Philosophy and the Three Figures of Syllogism

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Lecture Notes

Main Topics #

Humility as a Philosophical Prerequisite #

• Pride causes two kinds of errors in judgment: overestimating one’s own capability to judge, and failing to be docile (teachable) toward those genuinely wiser
• Thomas Aquinas exemplified docility by studying Augustine, Aristotle, and other great thinkers, thereby inheriting their wisdom
• Humility prevents the common error of setting up a straw man argument (“likeness is the cause of error”) and knocking it down to appear wise
• Great minds like Mozart demonstrate humility by studying their predecessors—Mozart studied Haydn extensively before composing his greatest works
• Without humility, one cannot be a good philosopher

The Division of Logic #

• Logic can be divided into the art of defining (definitio) and the art of reasoning (discursus)
• Definition provides knowledge of simple things (e.g., a square, virtue)
• Reasoning provides knowledge of statements one did not previously know
• Three ways of knowing whether a statement is true or false: (1) through the senses, (2) by understanding what the parts mean, (3) by formal logical necessity

If-Then Statements and Their Truth #

• An if-then statement’s truth does not require that both component simple statements be true
• Truth in an if-then statement means something different than truth in a simple statement
• Example: “If I’m a giraffe, then I have a long neck” is true, even though both components are false
• The if-then syllogism requires one if-then statement and one simple statement to produce a necessary conclusion
• Two valid forms of the if-then syllogism: (1) If A is so, then B is so; A is so; therefore B is so. (2) If A is so, then B is so; B is not so; therefore A is not so.
• Two invalid-looking forms that tempt errors: “If A is so, then B is so; A is not so; therefore B is not so” and “If A is so, then B is so; B is so; therefore A is so”
• An if-then statement can have true consequent even with false antecedent; what matters is the conditional relationship

Proving Invalidity vs. Proving Validity #

• One counterexample suffices to disprove a universal claim or show a form is invalid
• No number of confirming examples can prove a form is valid, because examples show only what sometimes happens, not what necessarily happens
• Necessity requires that something always be true; examples show only particular instances
• To prove invalidity, one need only find one instance where premises are true but conclusion false

The Three Figures of the Syllogism #

• A syllogism requires a middle term (B) that appears in both premises but not in the conclusion
• The middle term provides the necessary connection between premises
• First Figure: Middle term is predicate in major premise, subject in minor premise. Example: Every B is A; Every C is B; Therefore, every C is A. This is called “perfect” because the set of all (dici de omne) and set of none (dici de nulo) apply directly without conversion.
• Second Figure: Middle term is predicate in both premises. Cannot produce universal affirmative conclusions, only universal negatives. Called “imperfect” because conversion is required.
• Third Figure: Middle term is subject in both premises. Can only produce particular conclusions. Also requires conversion and “falls off” from universal to particular conclusions.

Why Aristotle Orders the Figures This Way #

• Aristotle places figures in order of their power and clarity
• The first figure is most powerful and obvious because set of all and set of none apply directly
• The second figure requires one conversion to reduce to the first figure
• The third figure requires conversion but yields only particular conclusions
• This ordering reflects the principle that we move from confused to distinct knowledge, from universal to particular

The Four Universal Cases #

• Within each figure, there are four possible combinations when both premises are universal:
  1. Both affirmative (universal affirmative premises)
  2. Both negative (universal negative premises)
  3. First affirmative, second negative
  4. First negative, second affirmative
• Total: 4 types × 4 combinations = 16 possible combinations per figure
• Across three figures: 16 × 3 = 48 total cases
• Not all 48 cases yield valid syllogisms

Why the Second Figure Cannot Produce Universal Affirmative Conclusions #

• In the second figure, the middle term is predicate in both premises
• The set of all requires that something be said to be the middle term universally
• Since nothing is said to be the middle term in the second figure, the set of all cannot apply directly
• Universal affirmative conversion loses power (“Every A is B” becomes “Some B is A”), dropping to particular
• Therefore, no universal affirmative conclusion is possible in the second figure

Why the Third Figure Cannot Produce Universal Conclusions #

• The middle term is subject in both premises
• When converting universal affirmatives to obtain the set of all, power is lost
• The conclusion can only be particular
• This is why the third figure “falls off” from universal to particular conclusions

Form vs. Matter in Logic #

• Aristotle places formal logic (Prior Analytics, dealing with form and A, B, C) before material logic (Posterior Analytics, dealing with specific matter and content)
• Form is prior to matter because man moves from confused to distinct knowledge
• The same formal structure can be valid or invalid regardless of content
• Examples: A dialectical argument and a demonstrative argument can have the same form but differ in whether premises are necessary or merely probable

The Definition of Syllogism #

• Syllogism: Speech in which some statements are laid down (posed firmly in the mind at rest), and another statement follows necessarily because of those laid down
• The metaphor of “laid down” parallels “laying down the law”—once laid down, the premises are firm and must be held in mind together
• If one lays down premises and then forgets them, no syllogism occurs; they must be held together in mind
• When premises are held firm and together, the conclusion must follow necessarily

Perfect vs. Imperfect Syllogisms #

• Perfect Syllogism: A syllogism where the necessity of the conclusion is obvious from the premises without requiring conversion. The set of all or set of none applies directly.
• Imperfect Syllogism: A syllogism where conversion of one or more premises is required to see that the conclusion follows necessarily. The necessity is not immediately obvious.
• The first figure contains the perfect syllogisms; the second and third figures contain imperfect syllogisms

Key Arguments #

The Necessity of the Middle Term #

• Each premise has a subject and predicate
• To syllogize, there must be a connection between premises
• The middle term (B) provides this connection by appearing in both premises
• Without a middle term relating the two premises, no syllogism is possible

Why Examples Cannot Prove Validity #

• To prove something is necessarily true or always true, one cannot rely on examples
• If man is necessarily white, then all men are white; but one black man disproves this
• Yet even unlimited numbers of white men do not prove all men are white
• The asymmetry shows that necessity cannot be established inductively
• A form is proven invalid by one counterexample, but proven valid only by understanding the logical form itself

Why Form Precedes Matter in Aristotle’s Ordering #

• Aristotle places Prior Analytics (formal logic) before Posterior Analytics (material logic)
• Man naturally moves from confused universal knowledge to distinct particular knowledge
• The same form is more universal than any particular matter
• Therefore, form is prior in the order of knowledge
• A dialectical and a demonstrative argument may have identical form but differ in the necessity of their premises

Important Definitions #

Syllogism (σύλλογος/syllogismos) #

Speech in which some statements are “laid down” (firmly posed in the mind), and another statement follows necessarily because of those laid down.

Perfect Syllogism (syllogismus perfectus) #

A syllogism where the necessity of the conclusion is obvious from the premises without requiring conversion; the set of all or set of none applies directly.

Imperfect Syllogism (syllogismus imperfectus) #

A syllogism where conversion of one or more premises is required to demonstrate that the conclusion follows necessarily.

Middle Term (terminus medius) #

The term appearing in both premises but not in the conclusion; provides the logical connection between major and minor terms.

Set of All (dici de omne) #

If something is said of all of a class, then whatever is a member of that class must have that property; basis for universal affirmative reasoning.

Set of None (dici de nullo) #

If something is said of none of a class, then whatever is a member of that class must not have that property; basis for universal negative reasoning.

Docility (from Latin docilis) #

The quality of being teachable; receptiveness to wisdom from those who are genuinely wiser; opposed to pride and necessary for philosophical progress.

Equivocal by Reason (aequivocum a ratione) #

A term that has one name applied to many things where there is an order or connection between the meanings.

Equivocal by Chance (aequivocum a casu) #

A term that has one name applied to many things where there is no connection or order between the meanings.

Examples & Illustrations #

Example of the First Figure (Perfect Syllogism) #

• Every animal is a substance (major premise)
• Every dog is an animal (minor premise)
• Therefore, every dog is a substance (conclusion)
• The set of all applies directly: whatever is said of all animals applies to whatever is a dog

Example of Invalid If-Then Reasoning #

• If the students in this room are four, then the students in this room are an even number (true if-then)
• The students in this room are four (true)
• Therefore, the students in this room are an even number (true conclusion)
• But if someone leaves: The students in this room are not four (true)
• Cannot conclude: The students in this room are not an even number (false—might be three, also odd, or two, also even)

Example Showing Truth in If-Then vs. Simple Statements #

• “If I’m a giraffe, then I have a long neck” — TRUE if-then statement, even though both parts are false
• “If I’m a mother, then I am a woman” — TRUE if-then statement
• In the if-then statement, truth means: “if the antecedent is true, the consequent must be true”
• In a simple statement, truth means: “what is, is; what is not, is not”

Counterexample Approach to Invalidity #

• Teacher proposes: “If student drops dead, student is absent from class”
• Student is absent from class
• Cannot conclude: Student dropped dead (car broke down, battery dead, etc.)
• Multiple possible causes show the form is invalid

Dante’s Ascent as Illustration of Simplicity and Perfection #

• As one ascends through the angelic hierarchies (lower to higher angels, then archangels, princes, virtues, powers, dominions, seraphim)
• The angels become simpler (fewer thoughts) yet more perfect (understand more deeply)
• This parallels the immaterial world: simplicity and perfection increase together
• God is most simple and most perfect—the endpoint of this ascent
• Contrasts with material world: stone is simpler than tree but less perfect; tree simpler than dog but less perfect

Mozart’s Humility #

• Mozart studied Haydn’s works extensively before composing his greatest quartets
• Dedicated his six greatest quartets (“Haydn Quartets”) to Haydn, saying “He taught me how to make a quartet”
• Haydn recognized Mozart’s superiority, telling Mozart’s father: “He is the greatest composer I know”
• Illustrates that genuine greatness includes docility and humility toward one’s predecessors

Aristotle’s Respect for Predecessors #

• Thomas Aquinas understood that “Aristotle means what Thomas says he means” shows how great philosophers interpret well
• Aristotle, when discussing “stupid interpretations” of earlier philosophers, never dismissed them without recalling what they said and why
• Aristotle would say: “Such a great philosopher and such a great matter—there must be some way of understanding this correctly; this person has misunderstood it”
• This approach contrasts with modern philosophers who simply contradict earlier thinkers without understanding their position

Ketcheny’s Remark on Thomas Aquinas #

• Ketcheny observed that Thomas so revered the Church Fathers that “he seemed to have inherited the mind of all of them”
• Illustrates how docility and humility toward great thinkers allows one to absorb and build upon their wisdom

Notable Quotes #

“If you don’t have humility, you’re going to be a bad philosopher.”

“Likeness is the cause of error.” (Shakespeare, The Comedy of Errors)

“A syllogism is speech in which some statements are laid down, and another follows necessarily because of those laid down.”

“You can’t prove by examples that a form is valid, because examples wouldn’t show that it’s always so, that it’s necessarily so. One example is enough to disprove it.”

“Understanding the statement and the meaning of the statement doesn’t tell you whether it’s true or false.”

“If something is necessarily so, then it’s always so. But it’s not always so, as my examples show. Therefore, it ain’t necessarily so. Therefore, it ain’t a syllogism.”

Questions Addressed #

How does pride lead to philosophical error? #

Answer: Pride causes two errors: (1) thinking oneself capable of judging matters beyond one’s knowledge, and (2) failing to be docile to those genuinely wiser. The solution is humility and docility toward great thinkers.

What distinguishes truth in an if-then statement from truth in a simple statement? #

Answer: In a simple statement, truth means “what is, is; what is not, is not.” In an if-then statement, truth means “if the antecedent is true, the consequent must be true”—not that either component is actually true. An if-then statement can be true even when both components are false.

Why can one counterexample disprove a form but no number of examples prove it valid? #

Answer: To disprove that something is always/necessarily true, one counterexample suffices. But to prove it is always/necessarily true requires understanding the form itself, not mere accumulation of instances. Examples show only what sometimes happens; necessity requires what always happens.

Why does Aristotle place the first figure before the second and third? #

Answer: The first figure is most powerful and obvious—the set of all and set of none apply directly without conversion. The second figure requires one conversion; the third requires conversion and yields only particular conclusions. This ordering reflects the natural movement from confused to distinct knowledge, from universal to particular.

Why can the second figure never produce a universal affirmative conclusion? #

Answer: In the second figure, the middle term is predicate in both premises. The set of all requires something to be universally predicated of the middle term, which cannot occur when the middle term is only in predicate position. Moreover, universal affirmative conversion loses power, dropping to particular.

Why can the third figure only produce particular conclusions? #

Answer: In the third figure, the middle term is subject in both premises. To get a universal conclusion would require converting a universal affirmative to maintain power, but such conversion loses power, dropping to particular. Therefore, conclusions must be particular.

What is the relationship between form and matter in logic? #

Answer: Form (the arrangement of terms) is prior to matter (specific content). Aristotle places formal logic (Prior Analytics) before material logic (Posterior Analytics) because man moves from confused universal knowledge to distinct particular knowledge. The same form is more universal than any particular matter.